“Self-starter” is an identity that up-and-coming leaders seek. It means that you take initiative and responsibility without being asked or coerced. You see a problem and you jump on it. No one ever has to tell you what to do. You put on your Nikes and just do it.
But there can be a dark side to self-starters, which is when their interest in beginning new projects and their disinterest in finishing projects are equal.